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According to these books, the first two sentences are perfectly correct, but there's a problem with the second sentence in the second pair. The rule says that the comparative form can only follow "# times"; in other words, it can never co-occur with "half" and "twice", though the two are also multiples. What do you think?

According to these books, the first two sentences are perfectly correct, but there's a problem with the second sentence in the second pair. The rule says that the comparative form can only follow "# times"; in other words, it can never co-occur with "half" and "twice", though the two are also multiples. What do you think?

***Not a teacher***

Yes I would agree with this.

These are acceptale:
'My room is twice the size of yours'
'My room is twice as big as yours'
and in theory:
'My room is two times the size of yours'
(not used in practice very often, as 'twice' is preferred)

According to these books, the first two sentences are perfectly correct, but there's a problem with the second sentence in the second pair. The rule says that the comparative form can only follow "# times"; in other words, it can never co-occur with "half" and "twice", though the two are also multiples. What do you think?

No, in general "Three times bigger" means "Four times as big". But because some people (and even grammar books) don't understand this concept, it's best not to use this phrase at all ("X times bigger").

(How much bigger than 100 is 400? 400 is four times as big as 100.
400 is also 300 bigger than 100, ie. three times 100 bigger than 100.
Four times as big = three times bigger.)